MECHANICAL ENGINEERING: Springs - connected in series, parallel

Hooke's law on springs:
Stretch is directly proportional to the Force

F = k S

where:

F = force applied

k = spring constant

S = stretch of spring




Springs connected in series


|
|               
|  
|-www-s1----www-s2----www-s3------> F
|               
|                
|                


S = s1 + s2 + s3



where:

S = total stretch of spring, equal to the sum of individual stretches of each spring s1, s2, s3

F = force applied 




Springs connected in parallel


|
|               
|   
|---wwww-k1----f1-|
|---wwww-k2----f2-|---> F
|---wwww-k3----f3-|
|               
|                
|                


if the springs are connected by a rigid bar, then

S = s1 = s2 = s3



sum of forces along x = 0; then 

F = f1 + f2 + f3


f1 = k1 * s1


where:

k1, k2, k3 = spring constants

S = total stretch of spring, equal to the sum of invidual stretches of each spring s1, s2, s3

F = force applied, equal to the individual forces on each springs